Quartile
المؤلف:
Freund, J. and Perles, B.
المصدر:
"A New Look at Quartiles of Ungrouped Data." American Stat. 41
الجزء والصفحة:
...
9-2-2021
3231
Quartile
One of the four divisions of observations which have been grouped into four equal-sized sets based on their statistical rank. The quartile including the top statistically ranked members is called the first quartile and denoted 
. The other quartiles are similarly denoted 
, 
, and 
. For 
data points with 
of the form 
(for 
, 1, ...), the hinges are identical to the first and third quartiles.
The following table summarizes a number of common methods for computing the position of the first and third quartiles from a sample size 
(P. Stikker, pers. comm., Jan. 24, 2005). In the table, ![[x]](https://mathworld.wolfram.com/images/equations/Quartile/Inline10.gif)
denotes the nearest integer function.
| method |
1st quartile |
1st quartile |
3rd quartile |
3rd quartile |
| |
 odd |
 even |
 odd |
 even |
| Minitab |
 |
 |
 |
 |
| Tukey (Hoaglin et al. 1983) |
 |
 |
 |
 |
| Moore and McCabe (2002) |
 |
 |
 |
 |
| Mendenhall and Sincich (1995) |
![[(n+1)/4]](https://mathworld.wolfram.com/images/equations/Quartile/Inline27.gif) |
![[(n+1)/4]](https://mathworld.wolfram.com/images/equations/Quartile/Inline28.gif) |
![[(3n+3)/4]](https://mathworld.wolfram.com/images/equations/Quartile/Inline29.gif) |
![[(3n+3)/4]](https://mathworld.wolfram.com/images/equations/Quartile/Inline30.gif) |
| Freund and Perles (1987) |
 |
 |
 |
 |
REFERENCES:
Freund, J. and Perles, B. "A New Look at Quartiles of Ungrouped Data." American Stat. 41, 200-203, 1987.
Hoaglin, D.; Mosteller, F.; and Tukey, J. (Ed.). Understanding Robust and Exploratory Data Analysis. New York: Wiley, pp. 39, 54, 62, 223, 1983.
Kenney, J. F. and Keeping, E. S. "Quartiles." §3.3 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 35-37, 1962.
Mendenhall, W. and Sincich, T. L. Statistics for Engineering and the Sciences, 4th ed. Prentice-Hall, 1995.
Moore, D. S. and McCabe, G. P. Introduction to the Practice of Statistics, 4th ed. New York: W. H. Freeman, 2002.
Whittaker, E. T. and Robinson, G. The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 184-186, 1967.
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